Conformal symmetries and classification in shear-free spherically symmetric spacetimes.

Abstract

In this thesis we study the conformal geometry of static and non-static spherically symmetric spacetimes. We analyse the general solution of the conformal Killing vector equation subject to integrability conditions which place restrictions on the metric func- tions. TheWeyl tensor is used to characterise the conformal geometry, and we calculate the Weyl tensor components for the spherically symmetric line element. The accuracy of our results is veri ed using Mathematica (Wolfram 2010) and Maple (2009). We show that the standard result in the conformal motions for static spacetimes is in- correct. This mistake is identi ed and corrected. Two nonlinear ordinary differential equations are derived in the classi cation of static spacetimes. Both equations are solved in general. Two nonlinear partial differential equations are derived in the classi- cation of non-static spacetimes. The rst equation is solved in general and the second equation admits a particular solution. Our treatment is the rst complete classi cation of conformal motions in static and non-static spherically symmetric spacetimes using the Weyl tensor.